1. Field of the Invention
The present disclosure generally relates to a cell image segmentation method and a nuclear-to-cytoplasmic ratio evaluation method using the cell image segmentation method and, more particularly, to a cell image segmentation method for cell segmentation and nuclear-to-cytoplasmic ratio analysis, as well as a nuclear-to-cytoplasmic ratio evaluation method using the same.
2. Description of the Related Art
Regarding conventional biopsy methodology and pathology examination, conventional methodology was achieved primarily through physical biopsy, which needs to remove a tissue from a living subject that is invasive, time-consuming, high-cost for preparation of abundant samples and evaluation at the microscopic level and also must be followed by complicated procedures including fixing, embedding, sectioning, and staining to determine the status of diseases. In addition to being painful to the patients, these invasive procedures may also result in risk of infection or even spreading of the cancer cells.
Optical in vivo virtual biopsy technique is successfully developed by our colleague, Ultrafast Optics Group (UFO), from National Taiwan University, which is a promising tool for noninvasive diagnosis and also can obtain in vivo section images in several skin depths. Without tissue removal, optical in vivo virtual biopsy can not only conquer the tedious stages in conventional invasive biopsy procedure, but also save time and cost for conventional pathology examination.
In order to evaluate the cell statuses, Nuclear-to-Cytoplasmic ratio (NC ratio) is a common measurement used in diagnosis and in vivo NC ratio analysis has its significance for non-invasive and immediate skin disease diagnosis. For example, the cell NC ratios of epidermis skin are in general larger as compared to those of normal cells in typical skin cancer.
FIG. 1 is conventional cell segmentation, including: (FIG. 1a) original image to be analyzed and (FIG. 1b) segmented cells. In FIG. 1a, the white areas “A” in the background represent cytoplasm, the black areas “B” surrounded by cytoplasm represent nuclei, and the enclosed lines “BND” represents cell boundaries. In FIG. 1b, the grey areas “D” represent segmented cytoplasm and the white areas “W” surrounded by segmented cytoplasm is segmented nuclei.
For conventional cell segmentation shown in FIG. 1, what it is required to do is select the nuclei and cytoplasm manually by hand selecting and then obtain the segmented nuclei and cytoplasm followed by NC ratio evaluation. It is time consuming, highly subjective, and also has inconsistent accuracy, especially for a huge mass amount of data to be analyzed.
Further conventional cell image processing methods are presented as the following:
Image thresholding is the simplest method with high-speed for image segmentation, but it has good segmentation results only for images with high contrast between objects and background. Illumination and noise are also factors to make image thresholding have undesired segmentation results even with adaptive thresholding methods. However, some biomedical images may have low contrast and contain lots of noise, which is not suitable to use image thresholding for cell segmentation.
FIG. 2 is an image segmentation of an image thresholding method, including: (FIG. 2a) input image and (FIG. 2b) result of segmentation with image thresholding of intensity. Referring to FIG. 2a, which is the input image to be analyzed, and its segmentation result with image thresholding of intensity is shown in (FIG. 2b), which has broken regions and interrupted boundary of detected objects. If the image thresholding of intensity is utilized for cell segmentation, it may not have expected results since this method does not consider the contextual information in the image and is susceptible to illumination and irregular noise which reduce the accuracy of segmentation.
Watershed transformation is one kind of image segmentation technique using the concept of morphological image processing to obtain stable segmentation results. The basic idea of watershed transformation can be considered as the phenomenon occurring on topographic surface. FIG. 3 is a topographic representation including: (FIG. 3a) two-dimensional gray-level image, and (FIG. 3b) three-dimensional topographic surface. FIG. 4 is a topographical view of the gray-level images. As shown in FIG. 3, a two-dimensional gray-level image can be considered as a three-dimensional topographic surface, that pixel values are interpreted as their altitude in the surface for watershed transformation. Three kinds of pixels including pixels at local minimum, at which a drop of water, and at which water would be equally likely to fall to more than one regional minimum are corresponding to regional minima, catchment basin, and watershed line, respectively in topographic view shown in FIG. 4.
Watershed transformation considering contextual information among pixels could be imagined that there is a hole connected with other holes by water pipe exists in each regional minimum and when the tap turned on, water from water source will flow through the pipe and then flood the surface from each regional minimum at a constant rate. The objective is to build a dam to prevent rising water spilling out from one catchment basin to another and the dam is corresponding to the segmented object. The main objective of watershed transformation is to identify the regions of regional minima with two stages. The first stage is flooding process to flood surface from regional minima and the second stage is dam construction to build barriers when two body of water from different basins meet together.
FIG. 5 is a flooding process of watershed transformation, including: (FIG. 5a) original topographic surface with four catchment basins, (FIG. 5b) topographic surface with water level is 90, (FIG. 5c) topographic surface with water level is 110, (FIG. 5d) topographic surface with water level is 130. FIG. 5 shows an example of flooding process with watershed transformation, wherein (FIG. 5a) shows original topographic surface with four catchment basins and the tap is turned on, the water level will start to rise up, and in (FIG. 5b) it can be seen that the water level is 90 and some regions are flooded, and in (FIG. 5c) water level raises to 110 and one body of water start to spill out to other one, so it needs to build a dam to prevent this thing from happening. If the water still rises, other dams should be built to prevent two distinct bodies of water meet together that shown in (FIG. 5d).
Using the above-mentioned ideas, watershed transformation often considers the gradient map and then can isolate or segment touching objects by identify the regional minima in the images. But over-segmentation problem is the main disadvantage that watershed transformation may meet since there may be some undesired regional minima or irregular noise in images and there are two main approaches to deal with the over-segmentation problem.
To solve the over-segmentation problem, the first approach to address the over-segmentation problem of watershed-based algorithm is fragment merging strategy to merge the tiny and fractional fragments of the same objects together by some merging criteria with the concept that the tiny fragments and their parent objects have the same or similar features.
The other approach to resolve the over-segmentation problem is marker-controlled strategy with assistance of marker map, including internal markers and external markers. The marker maps are the important information to direct the whole process of image segmentation to the path of obtaining segmented objects with high accuracy. The internal markers are like the seeds scattered on the whole image planes containing lots of peaks and valleys in topographic view. These seeds grow step by step with the guide of the watershed transformation to trend to gradually fit the size and shape of the objects to be segmented and with the restriction of the external markers to limit their ranges of growth and do not cross over the regions of other objects of interest.
Spectral clustering is one kind of technique for image segmentation that models the segmentation problem into the graph models as a weighted graph partitioning problem. Graph models can be built with some relations between the objects, such as similarities, distances, neighborhoods, connections, and so on. For example, vertices in the graph model can be considered as pixels in images and weighted edges connected between two vertices can be thought of as the similarity between two pixels with some criteria. Finding a cut through the graph model can be considered as finding meaningful groups of objects to resolve the problem of image segmentation and the concept of spectral clustering is also applied to cell segmentation to find meaningful objects. Although spectral clustering is a suitable approach for exploration of huge amount of data by graph modeling to reduce the complexity of the data to be analyzed, a desired graph model which can represent original data into the specific space with sparse matrix is an important topic it should be considered depending on different applications.
Deformable models which identify the boundaries of the object of interest by gradually development of contours or surfaces guided by internal and external forces are deformable curves with energy minimization to fit the image structures of interest adaptively. Several deformable models, like snake, balloon are utilized in cell segmentation. Since deformable models depend closely on several parameter settings, it may meet some difficulty to develop the algorithm for general applications. Additionally, deformable models are very sensitive to the initial condition and prior knowledge to have desirable segmentation results, which may not be possible especially for automatic cell segmentation. For example, for snake algorithm, the active contour is defined by user interactivity, which is sensitive to users intuition and initial guess that may be hard to have or decide automatically in most of applications.
Convergence index filters are local filters designed for edge or boundary enhancement in images with weak contrast and irregular noise caused by channel noise in front-end acquisition procedure, especially for biomedical images, which consider the distribution of the orientation of the gradient vectors instead of magnitude of the gradient vectors or intensity in spatial domain. The degree of convergence of the gradient vectors or called convergence index (CI) within the support region or neighborhood belonging to a pixel of interest is a measure of what degree of contribution the gradient vectors projected toward the pixel of interest. Additionally, convergence index filters own capability in adjusting the size and shape of their masks adaptively according to the distribution of the gradient vectors that make it possible to determine the boundaries of fuzzy regions in images. The following shows one of the types of filters.
Convergence index filters also called COIN filter named from acronym adopt a circle with variable radius as their support region. FIG. 6 is a support region of convergence index filter (CF). FIG. 6 shows a circle with radius r and its center is at pixel of interest P. The neighborhood of the pixel of interest P is denoted as R, which is the support region of pixel of interest P and we denote an arbitrary pixel Q whose Cartesian coordinate is (k,l) in R and θ is the angle between the gradient vector G(Q) at pixel Q and the direction of line segment PQ connecting pixel P and Q. cos θ(k,l) is used to represent the convergence index of the gradient vector G(Q) at pixel Q whose Cartesian coordinate is (k,l) that quantify the degree of contribution of this gradient vector G(Q) projected toward P.
The output of convergence index filter applying to pixel of interest P is defined as the average of the convergence indices at all pixels located in the support region R of pixel of interest P whose Cartesian coordinate is (x,y) and denoted in the following equation in 2-D discrete space,
            CF      ⁡              (                  x          ,          y                )              =                  1        M            ⁢                        ∑                                    (                              k                ,                l                            )                        ∈            R                                                          ⁢                  cos          ⁢                                          ⁢                      θ            ⁡                          (                              k                ,                l                            )                                            ,
where M is the number of pixels in the support region R, θ(k,l) is the angle between the gradient vector G(k,l) at pixel Q whose Cartesian coordinate is (k,l) and the direction of line segment PQ connecting pixel P and Q, and cos θ(k,l) is the convergence index of the gradient vector G(k,l) at pixel Q whose Cartesian coordinate is (k,l). The output of convergence filter locates between −1 and +1, and the maximum value of +1 happens when all gradient vectors of pixels in R point toward the pixel of interest P that means the equi-contours of intensity in R are concentric. FIG. 7 is a rounded convex region whose equi-contours of intensity are concentric, including: (FIG. 7a) a rounded convex region, and (FIG. 7b) the distribution of gradient vectors. FIG. 7a shows an example of rounded convex region whose equi-contours of intensity are concentric in 2-D space and FIG. 7b shows its distribution of gradient vectors that all gradient vectors is directed toward the center resulting in there is a maximum convergence index of +1 at the center of this rounded convex region. On the other hand, all gradient vectors of pixels in R point backward to the pixel of interest P will result in the minimum value of −1.